caa a22 4500 465743609 CHVBK 20180323111814.0 cr unu---uuuuu 170327e19900101xx s 000 0 eng 10.1007/BF01793786 doi (NATIONALLICENCE)springer-10.1007/BF01793786 On the existence of strongly normal ideals over P κ λ [Elektronische Daten] [Donna Carr, Jean Levinski, Donald Pelletier] For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $$\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$$ . Furthermore, < denotes the binary operation defined inP κ λ byx<y iffx⊂y∧¦x∣<¦y∩κ∣. By anideal over P κ λ we mean a proper, non-principal,κ-complete ideal overP κ λ extending the ideal dual to the filter generated by $$\left\{ {\left\{ {x \in P_\kappa \lambda :y \subseteqq x} \right\}:y \in P_\kappa \lambda } \right\}$$ . For any idealI overP κ λ,I + denotes the setP κ λ−I, andI * the filter dual toI. An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)<x}∈I + is constant on a set inI +. It is easy to see that every strongly normal ideal is normal. However, the converse of this is false. In this paper, we completely characterize those pairs (κ, λ) for whichP κ λ bears a strongly normal ideal, and describe the smallest such ideal for these pairs. As well, we show that for each of these pairs, the operator∇ < defined on the set of all ideals overP κ λ by where $$\nabla _< \left\{ {X_a :a \in P_\kappa \lambda } \right\} = \left\{ {x \in P_\kappa \lambda :x \cap \kappa = \phi \vee \left( {\exists a< x} \right)\left( {x \in X_a } \right)} \right\}$$ is idempotent. Our results include the following theorems. Springer-Verlag, 1990 primary 03E05 nationallicence secondary 03E55 nationallicence Carr Donna Department of Mathematics, University of Wisconsin Parkside, 53141, Kenosha, WI, USA aut Levinski Jean Department of Mathematics, Ohio University, 45701, Athens, OH, USA aut Pelletier Donald Department of Mathematics, York University, M3J1P3, North York, Ontario, Canada aut Archive for Mathematical Logic Springer-Verlag 30/1(1990-01-01), 59-72 0933-5846 30:1<59 1990 30 153 https://doi.org/10.1007/BF01793786 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01793786 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carr Donna Department of Mathematics, University of Wisconsin Parkside, 53141, Kenosha, WI, USA aut NATIONALLICENCE 700 1- Levinski Jean Department of Mathematics, Ohio University, 45701, Athens, OH, USA aut NATIONALLICENCE 700 1- Pelletier Donald Department of Mathematics, York University, M3J1P3, North York, Ontario, Canada aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 30/1(1990-01-01), 59-72 0933-5846 30:1<59 1990 30 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer